Electron. J. Differential Equations, Vol. 2016 (2016), No. 263, pp. 1-9.

A note on fractional supersolutions

Janne Korvenpaa, Tuomo Kuusi, Giampiero Palatucci

Abstract:
We study a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order s in (0,1) and summability growth p>1, whose model is the fractional p-Laplacian with measurable coefficients. We prove that the minimum of the corresponding weak supersolutions is a weak supersolution as well.

Submitted September 8, 2016. Published September 28, 2016.
Math Subject Classifications: 35D10, 35B45, 35B05, 35R05, 47G20, 60J75.
Key Words: Quasilinear nonlocal operators; fractional Sobolev spaces; fractional Laplacian; nonlocal tail; fractional superharmonic functions.

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Janne Korvenpaa
Department of Mathematics and Systems Analysis
Aalto University P.O. Box 1100
00076 Aalto, Finland
email: janne.korvenpaa@aalto.fi
Tuomo Kuusi
Department of Mathematics and Systems Analysis
Aalto University P.O. Box 1100
00076 Aalto, Finland
email: tuomo.kuusi@aalto.fi
Giampiero Palatucci
Dipartimento di Matematica e Informatica
Universita degli Studi di Parma
Campus - Parco Area delle Scienze, 53/A
43124 Parma, Italy
email: giampiero.palatucci@unipr.it

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